OFFSET
0,2
LINKS
Vincenzo Librandi, Table of n, a(n) for n = 0..229
Index entries for linear recurrences with constant coefficients, signature (483,-483,1).
FORMULA
For n > 1, a(n) = 482*a(n-1) - a(n-2) + 55. See A200993 for generalization.
From Bruno Berselli, Dec 21 2011: (Start)
G.f.: 55*x/((1-x)*(1-482*x+x^2)).
a(n) = a(-n-1) = 483*a(n-1)-483*a(n-2)+a(n-3).
a(n) = ((11-2*r)^(2*n+1)+(11+2*r)^(2*n+1)-22)/192, where r=sqrt(30). (End)
EXAMPLE
6*0 = 5*0;
6*55 = 5*66;
6*26565 = 5*31878;
6*12804330 = 5*15365196.
MATHEMATICA
LinearRecurrence[{483, -483, 1}, {0, 55, 26565}, 30] (* Vincenzo Librandi, Dec 22 2011 *)
PROG
(Maxima) makelist(expand(((11-2*sqrt(30))^(2*n+1)+(11+2*sqrt(30))^(2*n+1)-22)/192), n, 0, 11); /* Bruno Berselli, Dec 21 2011 */
(Magma) I:=[0, 55, 26565]; [n le 3 select I[n] else 483*Self(n-1)-483*Self(n-2)+Self(n-3): n in [1..15]]; // Vincenzo Librandi, Dec 22 2011
(PARI) concat(0, Vec(55/(1-x)/(1-482*x+x^2)+O(x^98))) \\ Charles R Greathouse IV, Dec 23 2011
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
Charlie Marion, Dec 20 2011
EXTENSIONS
a(11) corrected by Bruno Berselli, Dec 21 2011
a(6) corrected by Vincenzo Librandi, Dec 22 2011
STATUS
approved